How I Came by This Puzzle
Sometime in the late 1960s my father got a set of Heptiamonds for his birthday. He hardly gave it any thought but I, a boy of about nine, decided to give it a roll. Within a few hours I had found my first solution (picture right). I took a liking to this game and soon I got more such puzzles, with triangles, squares, hexagons in the pieces, in short, more Polyforms. But I've always liked that first one best, with the magical number of seven. And I still keep playing with the same battered old set.

Scratching the Surface
Even if I spend a lifetime chasing Heptiamonds problems, with or without software, I'm sure I'll cover only a tiny portion of the myriads of possibilities out there. As the Internet testifies, a small Polyform puzzle like Pentominoes still yields new discoveries. So I'll just keep this as a hobby on the side and do the Shapes I like best.

Why by Hand?
Although I have learned (long after my school days, that is) to appreciate the poetry in mathematics and although I admire the programmers who have written Polyforms solvers, I never have felt any urge to apply these tools myself. Time and again, I relish the gratifying moment when I fit the last piece into a particularly challenging configuration. Heptiamonds are my own little ‘Glass Bead Game’ (Hesse), with the same lack of practical value but providing a satisfaction comparable to listening a Bach fugue. You might say that my general approach to Polyforms is one of art rather than of science.

How I Find Them
Over the years, I have gained experience with how the puzzle pieces ‘behave’ and how they interact with each other within a certain Shape. Solving a Heptiamond problem, however, still boils down to intuition. All I can tell is that I hardly use any methods and that, like any ‘manual’ puzzler, I fiddle around with the pieces until they fit. Somehow, I seem to have an extra sense for this. Over time, I have devised some special challenges to keep things interesting:

Conscious Constraints
To puzzlers and mathematicians, these challenges may appear irrelevant but the reason to include them from time to time stems from my occasional design work with Polyforms, where repetitive combinations of puzzle pieces can become all too conspicuous. Let me show some examples of layouts I often try to avoid (but not always, or else my puzzles would become ‘monotonous’ again, or even unsolvable).

1 — Crosshairs. When assigning colors to the pieces, I prefer a maximum of three to meet at one point, in order to avoid intersecting a straight line as in the example (red). The exception is a point where three 60º corners come together on one side of a straight line (green check mark).

2 — Snake Den. The ‘long’ pieces catch the eye and often should be divided over the Shape, preferably in various orientations. Another thing I avoid is their frequent positioning along the edges of the Shape.

3 — Long Cut. Long straight divisions between pieces should be minimized, except, of course, where special Sub-Shapes are highlighted.

4 — Cronyism. Some specific puzzle pieces seem drawn to each other and form ubiquitous pairs. These are the two most notorious couples: a particular Fist and a particular Clover Leaf.

5 — Tastiest Bits Last. By getting rid of the ‘dogs’ quickly at the start, one seriously curbs one's creativity and thus the possibilities of solving a puzzle. In addition, one hardly gets to know the characteristics of the more difficult pieces and therefore will not progress to more advanced Shapes. In larger puzzles such as Octiamonds, a solution with the easy pieces concentrated in one area looks somehow unfinished to me.

About the Tessellations
After scanning the Internet for Heptiamond tessellations I gathered that there should exist a few more. I decided to try my hand at it, as a welcome excursion from solving Shapes. I am still unsure whether I would have followed through on this new venture, had I known what awaited me.

Yet some pesky little demon in the back of my head tells me that I have found mainly the obvious patterns and missed out on more exotic specimens. I'd be delighted to see others continue the quest and share their results online.

What we need here are sets of algorithms that define the tiling characteristics for every Heptiamond. Any takers?

The Drawings
All images on this page were created in Paint Shop Pro (Jasc Software). The solutions are transparent GIF images in Web Safe colors, a format which saves bytes. The example shows a small PSP window with part of a blown-up solution (Zoom function). The isometric grid is pretty accurate, a tad too wide but this deviation is negligible in regard to my purposes. It allows for a very systematical, uniform representation of Polyiamonds in crisp, compact images.

The Manufacturer
For those interested in brand names and puzzle history: my Heptiamonds are fuchsia-colored in a white case with a transparent lid and come from the Tenyo Company in Japan as No. 24 of a series of Polyforms and related brain teasers that bear the twin name of Computer Puzzle and Pla Puzzle. The side of one Basic Triangle is 1 cm. My set was issued before the catchy phrase Beat the Computer started to appear on the box, so I have a genuine ‘classic’ here.

Heptiamonds and Synesthesia
Do you see colors for letters or numbers, or perhaps for the days of the week or for the notes on the scale? I do, for all of the above. It's a phenomenon listed under the medical term Synesthesia and happens because the senses interplay. Hence such notions as ‘screaming colors’ or a symphony in ‘sage green E-Flat Major’.

Funny thing is: I also see pronounced colors for the Heptiamonds and only for these among all the Polyforms puzzles, although faint hues do occur occasionally. I have had this curious association as long as I remember, from my first solution onward, and the colors hardly have changed. Here's the first solution once more, in my coloring (colors may vary somewhat from screen to screen).

Would synesthesia help solve Heptiamonds with greater ease? I guess not, or else the other Polyforms puzzles would be noticeably harder for me. My special inclination towards Heptiamonds, however, may have to do with their enhanced individualization through colors. All in all, we may conclude that synesthesia has the same practical value as the puzzle itself (it does help me remember music though).

Make it Sew
— Negative, Captain: these have squares and are called Hexominoes.
— Yes, very well. And how much time do you think it takes to make such a patchwork ... kilt?
— Quilt, Sir. After replicating the cotton prints, I will require approximately three minutes twenty-five point two seconds when I use a period sewing machine. After careful consideration, I have decided to replicate a mid-1950s model Singer Feath...
— Thank you, Mr. Data, proceed. I can use something to cheer up my Ready Room.
— Aye, Sir.

— ... Engage!